CN104216924A - Time sequence index based on trends - Google Patents

Time sequence index based on trends Download PDF

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Publication number
CN104216924A
CN104216924A CN201310221588.9A CN201310221588A CN104216924A CN 104216924 A CN104216924 A CN 104216924A CN 201310221588 A CN201310221588 A CN 201310221588A CN 104216924 A CN104216924 A CN 104216924A
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trend
index
time series
time
interval
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肖瑞
刘国华
宋转
肖桂来
刘佩
张兵兵
张向
万小妹
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XIAORUI
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/22—Indexing; Data structures therefor; Storage structures
    • G06F16/2228—Indexing structures
    • G06F16/2246—Trees, e.g. B+trees
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/22—Indexing; Data structures therefor; Storage structures
    • G06F16/2228—Indexing structures
    • G06F16/2264—Multidimensional index structures
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/22—Indexing; Data structures therefor; Storage structures
    • G06F16/2228—Indexing structures
    • G06F16/2272—Management thereof

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  • Theoretical Computer Science (AREA)
  • Software Systems (AREA)
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  • Databases & Information Systems (AREA)
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  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Information Retrieval, Db Structures And Fs Structures Therefor (AREA)

Abstract

The invention provides an index mode based on change trends of time sequences (determined time sequences and undetermined time sequences) and first-order connectivity indexes, and the index mode has great significance to time sequence prediction, classification, data mining, knowledge discovery and the like. The index mode solves the problems of high data redundancy or low match accuracy and low index efficiency caused by the time sequence space indexes, precise query, similarity query, clustering and classification of the time sequences can be finished effectively through the index, and the time complexity and space complexity of sequence query, clustering and classification are lowered greatly. According to the index mode, firstly interval segmentation is conducted on the time sequences and time dimensions, short trend symbol sequences are generated in a mapping mode according to the change trends of the time sequences in all sections, then the first-order connectivity indexes of the section rising trend, section descending trend, section wave-crest trend, section wave-trough trend and section gentle trend are calculated for the symbol sequences, and finally a B-Tree index of a time sequence database is built by the adoption of the one-order indexes of the five trends.

Description

Based on the time series index of trend
Art
The present invention relates to a kind of seasonal effect in time series indexed mode, effectively can set up index to the time series in database, corresponding time series can be retrieved fast by this index, and support the similarity matching inquiry being completed sequence by this index.
Background technology
Because the data volume in time series databases is huge, in order to complete retrieval and similarity matching fast, need to set up index to time series.Due to seasonal effect in time series higher-dimension characteristic, and mostly theorem in Euclid space distance is adopted to Time Series Similarity tolerance, so its indexed mode also major part employing space index structure.Divide from large aspect, the spatial data index technique that time series adopts can be divided into tree construction (comprising R tree, K-D tree, quaternary tree) and grid file two class, mainly contain F-index, ST index, vp-tree, FastMap etc., but these indexing means cause very high data redundancy or reduce the accuracy of search efficiency and similarity matching.
Summary of the invention
In order to solve the problem that existing time series indexed mode data redudancy is high and index efficiency is low, this invention proposes a kind of indexed mode based on time series trend and single order Connectivity Index of Electronic Density, this indexed mode can according to seasonal effect in time series variation tendency, by the single order Connectivity Index of Electronic Density value of time series dimensionality reduction to 5 kind of Sequence Trend in polynomial time complexity, then by the single order Connectivity Index of Electronic Density of 5 kinds of trend, B-Tree index is set up to time series databases, thus realize setting up index to time series fast, and effective support carries out accurately inquiry and similarity matching inquiry by index.
The present invention solves the technical scheme that its problem adopts: to determining time series, first on time dimension, be divided into k isometric interval, then the sequence variation trend in each interval be mapped as a symbol in given trend assemble of symbol and by being trend symbol sebolic addressing according to sequential combination from left to right, finally trend symbol sebolic addressing calculated respectively to the single order Connectivity Index of Electronic Density of 5 kinds of trend symbols; To uncertain time sequence, first the observed value calculating each observation point is expected, builds the expectation sequence determined, then carries out interal separation, trend sign map to expectation sequence, and be combined as trend symbol sebolic addressing, finally calculate the single order Connectivity Index of Electronic Density of 5 kinds of trend symbols.To each time series, use this sequence of single order Connectivity Index of Electronic Density approximate representation of 5 kinds of trend symbols.Single order Connectivity Index of Electronic Density finally by certain trend symbol ts sets up B-Tree index, and in B-Tree, each leafy node comprises the single order Connectivity Index of Electronic Density of ts trend symbol and the single order Connectivity Index of Electronic Density of all the other 4 kinds of trend symbols; Realize accurately inquiring about seasonal effect in time series by the single order Connectivity Index of Electronic Density of comparison ts, by each leafy node of traversal B-Tree, and the Ta Nimote coefficient calculating the single order Connectivity Index of Electronic Density of two time serieses, 5 kinds of trend symbols completes similarity matching inquiry.
The invention has the beneficial effects as follows, can set up index fast and effectively to time series, this indexed mode support is carried out seasonal effect in time series by index and is accurately inquired about and inquire about with similarity matching.
Accompanying drawing explanation
Below in conjunction with accompanying drawing, the present invention is further described.
Fig. 1 the present invention relates to sequence exemplary plot of really fixing time.
Fig. 2 is the uncertain time sequence exemplary plot that the present invention relates to.
Fig. 3 is time series interal separation exemplary plot, interal separation example during time series L=10.
Fig. 4 is node types and node key element pie graph in the B-Tree index based on trend and single order Connectivity Index of Electronic Density.
Fig. 5 is the B-Tree index exemplary plot based on trend and single order Connectivity Index of Electronic Density.
Embodiment
Embodiment is mainly four parts, Part I realizes the Sequence Transformed expectation sequence for determining of uncertain time, Part II realizes interal separation and the trend sign map of expecting sequence, be combined as trend symbol sebolic addressing, Part III is the single order Connectivity Index of Electronic Density computation process of 5 kinds of trend symbols in trend symbol sebolic addressing, and Part IV is the B-Tree building process based on time series trend and single order Connectivity Index of Electronic Density.
First be Part I:
Determine that time series represents for each time point there being an ordered sequence determining sampled value; The uncertainty of uncertain time sequence is expressed as the set of the sample observations of each time point.The value of each time point represents by a stochastic variable, uncertain time sequence is thought the ordered sequence of the stochastic variable with time response.
Definition 1. (time series) length is that the time series of n is made up of the sequence that comprises n element, and time series is designated as: TS={ (t 1, X 1, P 1), (t 2, X 2, P 2) ..., (t n, X n, P n), wherein t irepresent i-th time point, the attribute variable X in every bar tuple tand P trepresent, X trepresent the set of t observed value, be designated as X t={ x t, 1, x t, 2..., x t, s, P trepresent the set of t observed value probability, be designated as P t={ p t, 1, p t, 2..., p t, s, s is set X tradix and the number of sample observation.
As s=1, TS represents and determines time series, and P t={ 1.0}.Determine that time series data collection is as shown in table 1.
When s ≠ 1, TS represents uncertain time sequence, and the data set of uncertain time sequence is as shown in table 2.
time values probability
1 {0.8} {1.0}
2 {1.1} {1.0}
3 … …
Time series data collection determined by table 1
time values probability
1 {0.8，0.9，1，1.5} {0.2，0.3，0.1，0.4}
2 {1.0，1.08，1.1} {0.28，0.37，0.35}
3 … …
Table 2 uncertain time sequence data collection
Being listed in the expectation of each observation point observed value by calculating uncertain time according to the order of sequence, uncertain time sequence being become the expectation sequence determined, i.e. TS exp={ (t 1, X 1.P 1), (t 2, X 2.P 2) ..., (t n, X n.P n), wherein X i.P i=x i, 1× p i, 1+ x i, 2× p i, 2+ ...+x i, s× p i, s(1≤i≤n), and the time series TS determined exp=TS.
Then be Part II:
Definition 2. (sequences segmentations) are the expectation sequence T of the time series T of n to length exp, according to the burst length L of segmentation, by T expbe divided into k=n/L isometric and continuous print interval, be designated as i respectively 1, i 2... .i k.If n ≠ k × L, then give up the Sequence of k × L+1 to n.Interval i jthe interval range of (1≤j≤k) is [(j-1) × L, j × L], interval i jthe lower boundary of (1≤j≤k) is designated as low (i j), coboundary is designated as high (i j), then L=high (i j)-low (i j), and for interval i j(1≤j < k), high (i j)=low (i j+1).
Definition 3. (interval trend) are the expectation sequence T of the time series T of n to length exp, after being divided into k isometric interval, T expat interval i jvariation tendency in (1≤j≤k) is interval trend, is designated as td j, td j∈ { td up, td dw, td st, td pk, td th, five kinds of interval trend are as shown in table 3, and interval trend and trend symbol one_to_one corresponding, trend assemble of symbol is correspondingly { ts up, ts dw, ts st, ts pk, ts th, wherein
(1) td upfor T expascendant trend is presented in cut section.
(2) td dwfor T expdowntrending is presented in cut section.
(3) td stfor T expsmooth trend is presented in cut section.
(4) td pkfor T exppeak value is obtained in cut section.
(5) td thfor T expvalley is obtained in cut section.
Definition 4. (trend sequence) are the expectation sequence T of the time series T of n to length expafter being divided into k isometric interval and judge the Sequence Trend in each interval, each interval is corresponding with an interval trend, and same each interval is corresponding with a trend symbol, trend symbol is connected from left to right successively for trend symbol sebolic addressing, is designated as SL (T)={ (i 1, ts 1), (i 2, ts 2) ..., (i k, ts k), wherein ts j∈ { ts up, ts dw, ts st, ts pk, ts th(1≤j≤k).
According to the burst length L of input, be the expectation sequence T of the time series T of n to length exptime dimension is divided into k=n/L interval, then to the interval starting point of each interval computation, the expectation sequence value V of interval intermediate point and interval end point 1, V 2, V 3, by the expectation sequence maximum occurrences V in these three values and this interval max, minimum value V mincarry out the trend of determination time sequence in this interval with trend factor alpha (0≤α≤0.5), interval Trend judgement method is as shown in table 3.Subsequently according to the mapping relations of trend symbol in interval interior seasonal effect in time series trend and trend assemble of symbol, obtain the trend symbol that time series is corresponding in this interval, invention defines the trend type of five kinds of sequences in interval, and each variation tendency is mapped as unique trend symbol, trend assemble of symbol S={ts up, ts dw, ts st, ts pk, ts th; Finally the trend symbol in each interval is connected to form symbol sebolic addressing SL (T)={ (i successively 1, ts 1), (i 2, ts 2) ..., (i k, ts k).The trend type of time series in certain interval and as shown in table 3 with the mapping relations of trend assemble of symbol interior element.
The Trend judgement of the interval j of table 3 (1≤j≤k) and sign map table
Next is Part III:
Definition 5. (trend positional information) length is the time series T of n, calculates acquisition trend symbol sebolic addressing SL (T), for each trend symbol ts m(1≤m≤5) and (ts m∈ { ts up, ts dw, ts st, ts pk, ts th) and SL (T) in each trend symbol ts j(1≤j≤k) and (ts j∈ { ts up, ts dw, ts st, ts pk, ts th), if ts m=ts j, then trend symbol ts mbe j/k in the positional information of position j; Trend symbol ts is obtained by traversal SL (T) mat whole positional information L of SL (T) t(ts m)=(L t, 1(ts m), L t, 2(ts m) ... L t, 1(ts m)), wherein 1 for meet ts in SL (T) m=ts jts jnumber.
Definition 6. (the single order Connectivity Index of Electronic Density of trend symbol) length is the time series T of n, trend symbol ts m(1≤m≤5) and (ts m∈ { ts up, ts dw, ts st, ts pk, ts th) single order Connectivity Index of Electronic Density IdT (ts m)=(L t, 1(ts m) × L t, 2(ts m)) -0.5+ (L t, 2(ts m) × L t, 3(ts m)) -0.5+ ...+(L t, 1-1(ts m) × L t, 1(tsm)) -0.5.
Time series T 1in five kinds of trend symbol ts up, ts dw, ts st, ts pk, ts thsingle order Connectivity Index of Electronic Density correspond to Id t1(ts up), Id t1(ts dw), Id t1(ts st), Id t1(ts pk), Id t1(ts th); Time series T 2in five kinds of trend symbol ts up, ts dw, ts st, ts pk, ts thsingle order Connectivity Index of Electronic Density correspond to Id t2(ts up), Id t2(ts dw), Id t2(ts st), Id t2(ts pk), Id t2(ts th); Then T 1and T 2similarity by Ta Nimote coefficient S t1, T2(S t1, T2∈ [0,1]) weigh, if S t1, T2> ε, T 1and T 2similar, otherwise two sequences are dissimilar, and wherein ε is similarity threshold.S t1, T2as shown in Equation 1.This similarity measurement is being undertaken by index using in Time Series Similarity match query.
S T 1 , T 2 = &Sigma; m = 1 5 Id T 1 ( ts m ) &times; Id T 2 ( ts m ) &Sigma; m = 1 5 Id 2 T 1 ( ts m ) + &Sigma; m = 1 5 Id 2 T 2 ( ts m ) - &Sigma; m = 1 5 Id T 1 ( ts m ) &times; Id T 2 ( ts m )
(ts m∈ { ts up, ts dw, ts pk, ts st, ts th) formula 1
To time series T, calculate five kinds of trend symbol ts up, ts dw, ts st, ts pk, ts thsingle order Connectivity Index of Electronic Density, be respectively: Id t(ts up), Id t(ts dw), Id t(ts st), Id t(ts pk), Id t(ts th).
Follow by Part IV:
Preset time arrangement set DS={T 1, T 2..., T m, wherein m is the size of arrangement set, T i={ (t 1, X 1, P 1), (t 2, X 2, P 2) ..., (t n, X n, P n) (1≤i≤m), calculate every bar time series T ithe single order Connectivity Index of Electronic Density of five kinds of trend symbols, and according to a kind of single order Connectivity Index of Electronic Density (such as Id of trend symbol t(ts dw)) building B-Tree index, the single order Connectivity Index of Electronic Density of all the other four kinds of trend symbols is stored in leafy node simultaneously.Each non-leaf nodes of the B-Tree index built comprises the set of key assignments and the set of pointer; Each leaf node comprises following information: (Id ti(ts dw), (Id ti(ts st), Id ti(ts up), Id ti(ts pk), Id ti(ts th)), P t), wherein P tfor the seasonal effect in time series address that this leaf node is corresponding.
Here is the B-Tree developing algorithm based on time series variation trend and single order Connectivity Index of Electronic Density:
Given time series q is accurately inquired about in time series databases D, first Id is calculated to q q(ts dw), then from the root node of B-Tree, if Id q(ts dw) in node, between two adjacent key assignments, then find corresponding subtree to continue to search according to the pointer after less key assignments; If Id q(ts dw) less than the key assignments of node, then find corresponding subtree to continue to search according to the pointer before this node key assignments; If Id q(ts dw) larger than the key assignments of node, then find corresponding subtree to continue to search according to the pointer after this node key assignments; If finally find leafy node, there is no key assignments and the Id of node q(ts dw) equal, then return sky, otherwise return the time series of this leafy node pointed.Can be obtained by the query time complexity of B-Tree, time complexity time series q being carried out in time series databases D to accurately inquiry is log 2m (), wherein m is seasonal effect in time series number in D.
At time series databases D, similarity query is carried out to given time series q, first Id is calculated to q q(ts dw), Id q(ts st), Id q(ts up), Id q(ts pk), Id q(ts th), then travel through the leaf node of whole B-Tree, and calculate the Ta Nimote coefficient of five kinds of trend symbol single order Connectivity Index of Electronic Density of sequence in q and each leafy node, if this coefficient is greater than ε, then this time series is added in results set.Need owing to performing similarity query each leafy node traveling through whole B-Tree, then the time complexity carrying out similarity query to given time series q in time series databases D is O (m), and wherein m is seasonal effect in time series number in D.

Claims (4)

1. one kind is carried out the indexed mode of effective index to time series (determining time series and uncertain time sequence).It is characterized in that: interal separation is carried out to time series time dimension, be mapped as trend symbol sebolic addressing according to the variation tendency of time series in each interval; To the single order Connectivity Index of Electronic Density of trend symbol sebolic addressing difference computation interval ascendant trend, interval downtrending, interval crest trend, interval trough trend, interval smooth trend, utilize the single order Connectivity Index of Electronic Density of any one trend type to build B-Tree index as unique index value, and the single order Connectivity Index of Electronic Density of all the other four kinds of trend is stored in the leafy node of B-Tree.
2. seasonal effect in time series indexed mode according to claim 1.It is characterized in that: adopt identical burst length to carry out interal separation to the time series in time series databases at time dimension, according to seasonal effect in time series variation tendency in five kinds of intervals of definition, trend in each interval is mapped as the symbol in a trend assemble of symbol, and according to time order and function order composition trend symbol sebolic addressing.
3. seasonal effect in time series indexed mode according to claim 1.It is characterized in that: single order Connectivity Index of Electronic Density trend symbol sebolic addressing being calculated respectively to five kinds of trend types, the single order connectivity sex index of trend type effectively retains the position feature of trend at trend symbol sebolic addressing, and build B-Tree index according to the single order Connectivity Index of Electronic Density of any one trend, the single order Connectivity Index of Electronic Density of all the other four kinds of trend is stored in the leafy node of B-Tree in a certain order simultaneously.
4. seasonal effect in time series indexed mode according to claim 1.It is characterized in that: by this index can the effectively accurate inquiry of deadline sequence, similarity query, seasonal effect in time series is accurately inquired about and is completed by the single order Connectivity Index of Electronic Density compared as index value, and seasonal effect in time series similarity query is by traveling through the leafy node of index and completing according to the Ta Nimote coefficient that the information that leafy node stores calculates two sequences, five kinds of trend.
CN201310221588.9A 2013-06-03 2013-06-03 Time sequence index based on trends Pending CN104216924A (en)

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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104933175A (en) * 2015-06-30 2015-09-23 深圳市金证科技股份有限公司 Performance data dependency analyzing method and performance monitoring system
CN105302867A (en) * 2015-09-28 2016-02-03 浙江宇视科技有限公司 Search engine check method and apparatus
CN105574128A (en) * 2015-12-12 2016-05-11 天津南大通用数据技术股份有限公司 Method for finishing complex data operations in business intelligence system
CN106844664A (en) * 2017-01-20 2017-06-13 北京理工大学 A kind of time series data index structuring method based on summary
CN109492028A (en) * 2018-11-09 2019-03-19 新疆工程学院 A kind of magnanimity time series data similarity join calculation method
CN113723201A (en) * 2021-08-03 2021-11-30 三明学院 Method, device and system for identifying time series local trend and storage medium
CN113961573A (en) * 2021-12-23 2022-01-21 北京力控元通科技有限公司 Time sequence database query method and query system
CN116955932A (en) * 2023-09-18 2023-10-27 北京天泽智云科技有限公司 Time sequence segmentation method and device based on trend

Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104933175A (en) * 2015-06-30 2015-09-23 深圳市金证科技股份有限公司 Performance data dependency analyzing method and performance monitoring system
CN104933175B (en) * 2015-06-30 2020-06-26 深圳市金证科技股份有限公司 Performance data correlation analysis method and performance monitoring system
CN105302867A (en) * 2015-09-28 2016-02-03 浙江宇视科技有限公司 Search engine check method and apparatus
CN105302867B (en) * 2015-09-28 2019-06-11 浙江宇视科技有限公司 A kind of search engine inquiry method and device
CN105574128A (en) * 2015-12-12 2016-05-11 天津南大通用数据技术股份有限公司 Method for finishing complex data operations in business intelligence system
CN106844664A (en) * 2017-01-20 2017-06-13 北京理工大学 A kind of time series data index structuring method based on summary
CN106844664B (en) * 2017-01-20 2020-04-17 北京理工大学 Time series data index construction method based on abstract
CN109492028A (en) * 2018-11-09 2019-03-19 新疆工程学院 A kind of magnanimity time series data similarity join calculation method
CN113723201A (en) * 2021-08-03 2021-11-30 三明学院 Method, device and system for identifying time series local trend and storage medium
CN113961573A (en) * 2021-12-23 2022-01-21 北京力控元通科技有限公司 Time sequence database query method and query system
CN116955932A (en) * 2023-09-18 2023-10-27 北京天泽智云科技有限公司 Time sequence segmentation method and device based on trend
CN116955932B (en) * 2023-09-18 2024-01-12 北京天泽智云科技有限公司 Time sequence segmentation method and device based on trend

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